Emilio Franco

FCT Researcher at CAMGSD, IST, U. Lisboa

emilio.franco@tecnico.ulisboa.pt

Phone (+351)218417086
Office 3.28
Mathematics Department
Instituto Superior Técnico
Avenida Rovisco Pais 1
1049-001 Lisboa
Portugal

Curriculum Vitae

Research Overview

Publications

Unramified covers and branes on the Hitchin system, with André Oliveira, Peter Gothen and Ana Peón-Nieto, Adv. Math. 377 (107493) (2021).
Involutions of the moduli spaces of G-Higgs bundles over elliptic curves, with Indranil Biswas, Luis Angel Calvo and Oscar Garcia-Prada, J. Geom. Phys. 142 (2019), 47-65.
Higgs bundles over elliptic curves for real groups, with Oscar Garcia-Prada and Peter Newstead, Quarterly J. Math. 70 (1) (2019), 105-146.
Higgs bundles over elliptic curves for complex reductive Lie groups, with Oscar Garcia-Prada and Peter Newstead, Glasgow Math. J. 61 (2) (2019), 297-320.
Brane involutions on irreducible holomorphic symplectic manifolds, with Marcos Jardim and Gregoire Menet, Kyoto J. Math. 59 (1) (2019), 195-235.
Moduli spaces of Lambda-modules on abelian varieties, with Pietro Tortella, Adv. Math. 318 (2017), 459-496.
Branes in the moduli space of framed instantons, with Marcos Jardim and Simone Marchesi, Bull. Sci. Math. 141 (4) (2017), 353-383.
Higgs bundles over elliptic curves, with Oscar Garcia-Prada and Peter Newstead, Illinois J. Math. 58 (1) (2014), 43-96.

Preprints

Degeneration of natural Lagrangians and Prymian integrable systems.
Deformation theory of orthogonal and symplectic sheaves.
The Borel subgroup and branes on the Hitchin system, with Ana Peón-Nieto.
Mirror symmetry for Nahm branes, with Marcos Jardim.

Research Interests

Geometry of moduli spaces and their role in mathematical physics. Mirror symmetry.

Students

PhD

Robert Hanson (IST, U. Lisboa), supported by La Caixa foundation.

Master

Pedro M. Silva (IST, U. Lisboa).
Joao Ruano (IST, U. Lisboa).

I am a tutor at the program "Nuevos Talentos em Matemáticas" of Gulbenkian Foundation.

Teaching

2nd semester 2021, Algebraic Geometry at IST (U. Lisboa).
2nd semester 2022 (scheduled), Galois Theory and Commutative Algebra at IST (U. Lisboa).

Seminars and events

I organize the Geometria em Lisboa seminar along with Rosa Sena-Dias.

Also, I belong to the organizing and scientific committe of the School on Mirror Symmetry and Moduli Spaces:

SMSMS 2021, 29th and 30th June 2021, online.
SMSMS 2022, 27th June to 1st July 2022, Lisbon.